Connecting two sphere with a cylinder
Here is a way to connect two spheres with a cylinder:

Create a cube, then in Edit mode, W Subdivide Smooth, and increase the subdivision with the parameters on the bottom of the T menu

Select a square and W &gt; LoopTools &gt; Circle

Make a hole, then extrude to create a circle inside the circle (E)

Duplicate your sphere and rotate the duplicate

Select the two holes and W &gt; LoopTools &gt; Bridge


After that you can add a Subdivision modifier, add edge loops to make the edge loops sharper, etc...